Fuzzy Solid Transportation Problem Research Articles

An efficient approach for solving type-2 intuitionistic fuzzy solid transportation problems with their equivalent crisp solid transportation problems

An efficient approach for solving type-2 intuitionistic fuzzy solid transportation problems with their equivalent crisp solid transportation problems

An extended Vogel’s approximation algorithm for efficiently solving Fermatean fuzzy solid transportation problems

An extended Vogel’s approximation algorithm for efficiently solving Fermatean fuzzy solid transportation problems

A NOVEL METHOD FOR SOLVING FULLY FUZZY SOLID TRANSPORTATIONS PROBLEMS

In this paper, we proposes a new method for solving solid transportation problem under uncertainty environments. The fully fuzzy solid transportation problem has been formulated. To reduce the model into crisp equivalent, we have used existing method for approximation of fuzzy numbers by interval numbers and its arithmatics. A simplex method and existing method for solving Interval Linear Programming problems are used for solving solid transportation problem with fuzzy parameters and decision variables. Furthermore, for illustration, some numerical examples are used to demonstrate the correctness and usefulness of the proposed method. The proposed algorithm is flexible, easy and reasonable.

A Systematic Formulation into Neutrosophic Z Methodologies for Symmetrical and Asymmetrical Transportation Problem Challenges

This study formulates a multi-objective, multi-item solid transportation issue with parameters that are neutrosophic Z-number fuzzy variables such as transportation costs, supplies, and demands. This work covers two scenarios where uncertainty in the problem can arise: the fuzzy solid transportation problem and the interval solid transportation problem. The first scenario arises when we represent data problems as intervals instead of exact values, while the second scenario arises when the information is not entirely clear. We address both models when the uncertainty alone impacts the constraint set. In order to find a solution for the interval case, we generate an additional problem. Since this auxiliary problem is typical of solid transportation, we can resolve it using the effective techniques currently in use. In the fuzzy scenario, a parametric method is used to discover a fuzzy solution to the earlier issue. Parametric analysis identifies that the best parameterized approaches to complementary problems are characterized by the application of parametric analysis. We present a suggested algorithm for determining the stability set. Finally, we provide a numerical example and sensitivity analysis for the transportation problem, which is both symmetrical and asymmetrical.

Multi-goal Multi-product Fuzzy Solid Transportation Problem via Goal Programming Technique

Multi-goal Multi-product Fuzzy Solid Transportation Problem via Goal Programming Technique

PSK Method for Solving Mixed and Type-4 Intuitionistic Fuzzy Solid Transportation Problems

In this article, the author categorises the solid transportation problem (STP) under uncertain environments. He formulates the mixed and fully intuitionistic fuzzy solid transportation problems (FIFSTPs) and utilizes the triangular intuitionistic fuzzy number (TIFN) to deal with uncertainty and hesitation. The PSK (P. Senthil Kumar) method for finding an intuitionistic fuzzy optimal solution for fully intuitionistic fuzzy transportation problem (FIFTP) is extended to solve the mixed and type-4 IFSTP and the optimal objective value of mixed and type-4 IFSTP is obtained in terms of triangular intuitionistic fuzzy number (TIFN). The main advantage of this method is that the optimal solution of mixed and type-4 IFSTP is obtained without using the basic feasible solution and the method of testing optimality. Moreover, the proposed method is computationally very simple and easy to understand. Finally, the procedure for the proposed method is illustrated with the help of numerical examples which is followed by graphical representation of the finding.

PSK Method for Solving Intuitionistic Fuzzy Solid Transportation Problems

This article proposes a method for solving intuitionistic fuzzy solid transportation problems (IFSTPs) in which only the transportation costs are represented in terms of intuitionistic fuzzy numbers (IFNs). The remaining parameters, namely: supply, demand and conveyance capacity, are all considered into crisp numbers. This type of STP is called a type-2 IFSTP. When solving the real life solid transportation problems (STPs) those tend to face the uncertainty state as well as hesitation due to many uncontrollable factors. To deal with uncertainty and hesitation many authors have suggested the intuitionistic fuzzy representation for the data. In this article, the author tried to categorise the STPs under the uncertain environment. He formulates the intuitionistic fuzzy STPs and utilizes the triangular intuitionistic fuzzy number (TIFN) to deal with uncertainty and hesitation. The PSK (P.Senthil Kumar) method for finding an intuitionistic fuzzy optimal solution for fully intuitionistic fuzzy transportation problem (FIFTP) is extended to solve the type-2 IFSTP and the optimal objective value of type-2 IFSTP is obtained in terms of TIFN. The main advantage of this method is that the optimal solution of type-2 IFSTP is obtained without using the basic feasible solution and the method of testing optimality. Moreover, the proposed method is computationally very simple and easy to understand. A case study is presented to illustrate the procedure of the proposed method.

A Simple and Efficient Algorithm for Solving Type-1 Intuitionistic Fuzzy Solid Transportation Problems

This article describes how in solving real-life solid transportation problems (STPs) we often face the state of uncertainty as well as hesitation due to various uncontrollable factors. To deal with uncertainty and hesitation, many authors have suggested the intuitionistic fuzzy (IF) representation for the data. In this article, the author tried to categorise the STP under uncertain environment. He formulates the intuitionistic fuzzy solid transportation problem (IFSTP) and utilizes the triangular intuitionistic fuzzy number (TIFN) to deal with uncertainty and hesitation. The STP has uncertainty and hesitation in supply, demand, capacity of different modes of transport celled conveyance and when it has crisp cost it is known as IFSTP of type-1. From this concept, the generalized mathematical model for type-1 IFSTP is explained. To find out the optimal solution to type-1 IFSTPs, a single stage method called intuitionistic fuzzy min-zero min-cost method is presented. A real-life numerical example is presented to clarify the idea of the proposed method. Moreover, results and discussions, advantages of the proposed method, and future works are presented. The main advantage of the proposed method is that the optimal solution of type-1 IFSTP is obtained without using the basic feasible solution and the method of testing optimality.

Sensitivity Analysis of Intuitionistic Fuzzy Solid Transportation Problem

This paper focuses on sensitivity analysis of intuitionistic fuzzy solid transportation problem (IFSTP). In real-world situation, IFSTP seems to be more realistic than solid transportation problem (STP) as available information is uncertain. Due to degeneracy of IFSTP or that of STP, Type I sensitivity analysis seems to be impractical. Hence , in this paper, a new algorithm is proposed to determine the Type II sensitivity ranges to overcome this problem. A numerical example is illustrated to demonstrate the feasibility of the proposed algorithm and the efficiency of recommended method over existing method.

Solving Intuitionistic Fuzzy Solid Transportation Problem Via New Ranking Method Based on Signed Distance

In this paper, signed distance of Symmetrical Intuitionistic Fuzzy Numbers (SIFNs) is introduced. Based on this signed distance and the crisp ranking system on real numbers, a new ranking system for SIFNs is defined, which seems to be very realistic. To illustrate the applicability and suitability of the proposed ranking method and to deal with ambiguity and imprecision, one of the vital mathematical programming problem viz. Solid Transportation Problem (STP) is formulated in intuitionistic fuzzy environment. A new method has been proposed to compute initial basic feasible solution for the same. Also the significance of the proposed approach over existing methods is illustrated. Finally numerical examples are solved to demonstrate the efficiency of the proposed methods.

A simple parametric method to generate all optimal solutions of fuzzy solid transportation problem

This paper deals with the fuzzy solid transportation problem (FSTP) that has fuzzy cost coefficients, fuzzy supplies, fuzzy demands and fuzzy conveyances. All these fuzzy quantities of FSTP are assumed to be triangular fuzzy numbers. For this problem, we propose an approach to generate all optimal solutions parametrically. The first stage of our approach is to determine the feasibility range based on fuzzy supply–demand–conveyance quantities. In the second stage, the breaking points of fuzzy costs are found by intersecting the membership functions of the fuzzy costs. The last stage constructs the optimal solutions of FSTP by means of some proposed auxiliary programs. Also a numerical example has been provided to illustrate our solution procedure.

English

English

Fully fuzzy fixed charge multi-item solid transportation problem

This paper presents fully fuzzy fixed charge multi-item solid transportation problems (FFFCMISTPs), in which direct costs, fixed charges, supplies, demands, conveyance capacities and transported quantities (decision variables) are fuzzy in nature. Objective is to minimize the total fuzzy cost under fuzzy decision variables. In this paper, some approaches are proposed to find the fully fuzzy transported amounts for a fuzzy solid transportation problem (FSTP). Proposed approaches are applicable for both balanced and unbalanced FFFCMISTPs. Another fuzzy fixed charge multi-item solid transportation problem (FFCMISTP) in which transported amounts (decision variables) are not fuzzy is also presented and solved by some other techniques. The models are illustrated with numerical examples and nature of the solutions is discussed.

Fractional Goal Programming for Fuzzy Solid Transportation Problem with Interval Cost

In this paper, we study a solid transportation problem with interval cost using fractional goal programming approach (FGP). In real life applications of the FGP problem with multiple objectives, it is difficult for the decision-maker(s) to determine the goal value of each objective precisely as the goal values are imprecise, vague, or uncertain. Therefore, a fuzzy goal programming model is developed for this purpose. The proposed model presents an application of fuzzy goal programming to the solid transportation problem. Also, we use a special type of non-linear (hyperbolic) membership functions to solve multi-objective transportation problem. It gives an optimal compromise solution. The proposed model is illustrated by using an example.

A solid transportation problem with type-2 fuzzy variables

This paper focuses on generating the optimal solutions of the solid transportation problem under fuzzy environment, in which the supply capacities, demands and transportation capacities are supposed to be type-2 fuzzy variables due to the instinctive imprecision. In order to model the problem within the framework of the credibility optimization, three types of new defuzzification criteria, i.e., optimistic value criterion, pessimistic value criterion and expected value criterion, are proposed for type-2 fuzzy variables. Then, the multi-fold fuzzy solid transportation problem is reformulated as the chance-constrained programming model with the least expected transportation cost. To solve the model, fuzzy simulation based tabu search algorithm is designed to seek approximate optimal solutions. Numerical experiments are implemented to illustrate the application and effectiveness of the proposed approaches.

Optimal way of selecting cities and conveyances for supplying coal in uncertain environment

In this paper, the limitations and shortcomings of the existing methods for solving fuzzy solid transportation problem are pointed out and to overcome these shortcomings, a new method is proposed for solving fuzzy solid transportation problem. The advantages of the proposed method over the existing methods are discussed. To illustrate the proposed method, an existing fuzzy solid transportation problem is solved. Also, to show the application of the proposed method in real life problems an existing real life fuzzy solid transportation problem is solved by the proposed method.

Fuzzy total transportation cost measures for fuzzy solid transportation problem

The solid transportation problem considers the supply, the demand, and the conveyance to satisfy the transportation requirement in a cost-effective manner. This paper develops a method that is able to derive the fuzzy objective value of the fuzzy solid transportation problem when the cost coefficients, the supply and demand quantities and conveyance capacities are fuzzy numbers. Based on the extension principle, the fuzzy solid transportation problem is transformed into a pair of mathematical programs that is employed to calculate the lower and upper bounds of the fuzzy total transportation cost at possibility level α. From different values of α, the membership function of the objective value is approximated. Since the objective value is fuzzy, the values of the decision variables derived in this paper are fuzzy as well. An example is illustrated for the whole idea.

Solving fuzzy solid transportation problems by an evolutionary algorithm based parametric approach

The Solid Transportation Problem (STP) arises when bounds are given on three item properties. The Fuzzy Solid Transportation Problem (FSTP) appears when the nature of the data problem is fuzzy. This paper deals with the FSTP in the case in which the fuzziness affects the constraint set, and a fuzzy solution to the problem is required. Moreover, an arbitrary linear or nonlinear objective function is considered. In order to find a fuzzy solution to the problem, a parametric approach is used to obtain an auxiliary Parametric Solid Transportation Problem (PSTP) associated to the original problem. As there are no well-known solution methods proposed in literature to solve effectively the PSTP, in this paper an Evolutionary Algorithm (EA) based solution method is proposed to solve it, which can finally be applied to find a “good” fuzzy solution to the FSTP. Comparisons with another conventional method are presented and the results show the EA based approach to be better as a whole.

Uncertain solid transportation problems

The solid transportation problem arises when bounds are given on three item properties. Usually, these properties are source, destination and type of product or mode of transport, and often are given in a uncertain way. This paper deals with two of the ways in which uncertainty can appear in the problem: Interval solid transportation problem and fuzzy solid transportation problem. The first arises when data problem are expressed as intervals instead of point values, and the second when the nature of the information is vague. Both models are treated in the case in which the uncertainty affects only the constraint set. For interval case, an auxiliary problem is obtained in order to find a solution. This auxiliary problem is a standard solid transportation problem which can be solved with the efficient methods existing. For fuzzy case, a parametric approach which makes it possible to find a fuzzy solution to the former problem is used.